Angular Fourier Series descriptors

To reproduce the results of Machine learning surrogate models for prediction of point defect vibrational entropy. Python implementation of the chemical environment descriptor Angular Fourier Series defined in the paper On representing chemical environments by Bartok, Kondor, Csanyi.

Dependencies

• python3 >= 3.6 (for f strings)
• numpy >= 1.15
• scipy >= 1.4
• scikit-learn >= 0.19

Implementation details

• Periodic boundary condition are handled via replication of the atomic positions.
• Atom neighbors search are done using scipy.spatial.cKDTree.
• Square root of the scalar product matrix ( formula (25) section III.D, page 7 in the paper 'On representing chemical environments') is computed via diagonalization using scipy. Regularization term is added on the diagonal to prevent from small negative eigenvalues (magnitude ~ 1e-16) due to numerical artifacts.
• Computations are vectorized using numpy functions.

Usage

To reproduce the results in figure 2 of the paper 'Machine learning surrogate ...' for EAM database, run

python main.py --database EAM --l_max 10 --n_max 20 --r_cut 5.

and for MEAM database, run

python main.py --database MEAM --l_max 10 --n_max 20 --r_cut 5.

If you use this work, please cite :

@article{lapointe2020machine,
  title={Machine learning surrogate models for prediction of point defect vibrational entropy},
  author={Lapointe, Clovis and Swinburne, Thomas D and Thiry, Louis and Mallat, St{\'e}phane and Proville, Laurent and Becquart, Charlotte S and Marinica, Mihai-Cosmin},
  journal={Physical Review Materials},
  volume={4},
  number={6},
  pages={063802},
  year={2020},
  publisher={APS}
}